A166930 Positive integers m such that m^4 = a^2 + b^2 and a + b = c^2 for some positive coprime integers a, b, c.

2165017, 15512114571284835412957, 368440923990671763222767414151367493861848396861, 29032470413228645503712143213832535500985227130245791625262982715784415755764157625

Offset: 1

Author

Max Alekseyev, Oct 23 2009

Keywords

• nonn

Comments

Square roots of the hypotenuses of Pythagorean triangles in which the hypotenuse and the sum of the legs are squares. In a letter to Mersenne in the year 1643, Fermat asserted that the smallest such triangle has the legs 4565486027761 and 1061652293520, and the hypotenuse a(1)^2 = 4687298610289.

Subsequence of A166929 which allows a,b be nonzero.

Values of m in coprime solutions to 2m^4 = c^4 + d^2 with d < c^2 (so that a,b = (c^2 +- d)/2). Corresponding values of c are given in A167438.

References

• W. Sierpinski. Pythagorean Triangles. Dover Publications, 2003, ISBN 0-486-43278-5.

Links

• Gerry Martens, Table of n, a(n) for n = 1..13

Crossrefs

Cf. A166929, A167437, A167438.

Extensions

Edited by Max Alekseyev, Nov 03 2009